Question

A carousel has a diameter of 10 m. How far (path length) does little Joey, strapped in at the very edge of the carousel, travel if the carousel is rotated through angle of 45 degrees, 45 rad and 45 rev, respectively?

Answer 1

circumference = 2 pi R = pi D
= 31.4 meters

45 deg = 360/8 so 31.4/8 meters

45 rad = 45/(2 pi) circles = 7.162 circles
7.162 * 31.4 = 225 meters

45 circles
45 * 31.4 = 1413 meters